PROJECT SUMMARY. This project involves the development of statistical methodology for the analysis of large- scale genomic data, such as gene expression, DNA copy number, and DNA sequencing data. In genomic studies, the goal is often to identify signal in the data in an unsupervised way. For instance, given the gene expression measurements for a set of patients with lung cancer, one might wish to discover previously unknown lung cancer subtypes that are characterized by distinct gene expression signatures and that might differ with respect to prognosis or response to therapy. However, the search for signal in genomic data is made difficult by the fact that the number of variables (e.g. genes) is generally orders of magnitude greater than the number of observations (e.g. lung cancer patients). As a result, principled methods must be developed to discover signal without overfitting. Furthermore, there is a need for objective ways to assess the validity of results obtained. This proposal has four specific aims, each of which involves the development of a new statistical method for solving a problem that arises in the analysis of genomic data. Aim 1: A method to learn multiple related genomic networks at once. For instance, one might expect that the gene expression networks for cancer and normal tissues will look similar to each other, with certain specific differences. The current proposal will provide a way to learn both networks simultaneously, in order to identify gene pathways that are perturbed in cancer. The proposed approach involves applying shrinkage penalties to the Gaussian graphical model formulation for network estimation. Aim 2: A principled approach for simultaneously clustering the rows and columns of a data matrix (e.g. patients and genes). The standard approach for discovering signal in genomic data involves clustering rows and columns independently, but the proposed approach will have increased power to discover biologically relevant clusters. The proposed approach involves applying shrinkage penalties to the matrix-variate normal distribution. Aim 3: A tool for the integrative analysis of multiple genomic data types collected on a single set of patient samples. For instance, if gene expression data, copy number data, and methylation data are collected for a single set of samples, then this will allow for the discovery of subsets of patients that are characterized by particular signatures of gene expression, copy number variation, and methylation. This could lead to the discovery of clinically relevant subtypes of cancer and other diseases. The proposed approach is an extension of the approach described in Aim 2. Aim 4: A flexible framework for the validation of clusters discovered in structured genomic data, such as DNA copy number and single nucleotide polymorphism data, in order to determine whether clusters discovered reflect signal or simply noise. The proposed approach is related to cross-validation, and will be extended to develop a method for the validation of other unsupervised statistical tools, such as those described in Aims 1-3 above. The statistical tools that result from the proposed research will be implemented in freely available software.